Please help, I'm finding difficulty in this math problem

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I'm finding difficulty in Solving this :

H (x) = 1/ 4√x^2 - 5x

I am extremely uncertain what you are asking. You have basically just stating a function, I'm sure what you want me to do.

Isn't it actually H(x)=- 4 3/4x (aka -4,75x)?
√x^2 = x because square power(^2) and square root(√) annihilate each other.

H (x) = 1/ 4√x^2 - 5x
H (x) = 1/ 4x - 5x
H (x) = - 4 3/4x
H (x)= -4,75x

In that case this if a line function.
y=0
0=-4,75x |:-4,75
x=0/-4,75=0

^ counting the x where function has value of 0 (y=0) aka where it crosses x line.
(point 0,0)

x=0
y=-4,75*0=0

^ counting the y value for x=0 aka where it crosess y line.
(point 0,0)

It crosses line the x and y lines in just one point: (0,0)

x=1
y=-4,75*1=-4,75
It passes point (1,-4,75)

As you put the 2 points (0,0), (1,-4,75) on the chart and connect them you will see it is a descending line function (I might call it wrong because I am translating the name from Polish).
It will be similar to this one but slightly more steep:



Unless the whole thing is under 1, but then it should be written as H (x) = 1/(4√x^2 - 5x).
Then the answer would be:
H (x) = 1/(4√x^2 - 5x)
H (x) = 1/(4x - 5x)
H (x) = - 1/x

In that case:
y=0
0=-1/x |*x
0x=-1
0=-1 WRONG!! 0 isn't -1
It never crosses line x (no point with y=0)

x=0
y=-1/0 WRONG!! Never divide by 0!
It never crosses line y (no point with x=0)

x=1
y=-1/1
y=-1
point (1,-1)
x=-1
y=-1/-1
y=1
point (-1,1)
x=-2
y=-1/-2
y=0,5
point (-2, 0,5)
x=-0,5
y=-1/-0,5
y=2
point (-0,5,2)
and so on.

After putting enough points on chart (like this: http://www.matmana6.pl/zdjecia/szkola_s ... a_x_10.PNG) you will see the function is inverted hiperbole.
Similar to this one but with different values:



I hope it helped. I might have made some mistakes because last time I had to deal with examples like this was 8 years ago. And I used Polish then.

Entertaining thread, complete with a twist ending for anyone who wasn't paying close attention through the main exposition.

I wonder if it answered the highly obscure question of the OP?